1. Field of the Invention
This invention relates to an active filter which can be used as various filters for a video signal or audio signal frequency band.
2. Description of the Related Art
An active filter is known as a filter whose size and weight can be easily reduced. The active filter is a circuit formed of a combination of an operational amplifier, resistor element and capacitor element.
FIG. 3 is an equivalent circuit diagram showing the construction of the conventional active filter. An input terminal IN is connected to the input terminal of an amplifier 31 and the non-inverting input terminal of a current differential amplifier (which is hereinafter referred to as a gm amplifier) 32. The output terminal of the amplifier 31 is connected to an output terminal of the gm amplifier 32 and an output terminal OUT via a capacitor Co. Further, the output terminal of the gm amplifier 32 is connected to the inverting input terminal of the gm amplifier 32.
FIG. 4 is a circuit diagram showing the concrete construction of the above equivalent circuit and an area surrounded by broken lines on the left hand side indicates the amplifier 31 and an area on the right hand side indicates the gm amplifier 32.
In the amplifier 31, the base of a transistor Q.sub.7 is connected to the input terminal IN. The collector of the transistor Q.sub.7 is connected to a power source Vcc and the emitter thereof is connected to the emitter of a transistor Q.sub.8 via a resistor R.sub.3 and to the ground potential Vss via a constant current source I.sub.4. The emitter of the transistor Q.sub.8 is connected to the ground potential Vss via a constant current source I.sub.5 and the base thereof is connected to the ground potential Vss via a reference power source Vo. Further, the collector of the transistor Q.sub.8 is connected to the power source Vcc via a resistor R.sub.4 and to the base of a transistor Q.sub.9. The collector of the transistor Q.sub.9 is connected to the power source Vcc and the emitter thereof is connected to the ground potential Vss via a constant current source I.sub.6.
In the gm amplifier 32, the base of a transistor Q.sub.1 is connected to the input terminal IN. The collector of the transistor Q.sub.1 is connected to the power source Vcc and the emitter thereof is connected to the collector and base of a transistor Q.sub.2 via a resistor R1 and to the base of a transistor Q.sub.3 via a resistor R1. The emitter of the transistor Q.sub.2 is connected to the ground potential Vss via a constant current source I.sub.1 and to the emitter of a transistor Q.sub.6. The collector of the transistor Q.sub.3 is connected to the power source Vcc and the emitter thereof is connected to the emitter of a transistor Q.sub.4 and to the ground potential Vss via a constant current source I.sub.2. The collector of the transistor Q.sub.4 is connected to the emitter of the transistor Q.sub.9 of the amplifier 31 via the capacitor Co and to the power source Vcc via a constant current source I.sub.3. Further, the collector of the transistor Q.sub.4 is connected to the base of a transistor Q.sub.5 and to the output terminal OUT. The collector of the transistor Q.sub.5 is connected to the power source Vcc and the emitter thereof is connected to the collector and base of the transistor Q.sub.6 via a resistor R.sub.2 and to the base of the transistor Q.sub.3 via a resistor R2.
With the above construction, a signal voltage supplied to the input terminal IN is converted into current by means of the gm amplifier 32 and the capacitor Co is charged or discharged by the converted current. At the same time, the capacitor Co is applied with a voltage corresponding to a signal voltage supplied to the input terminal IN via the amplifier 31. As a result, a voltage obtained by adding a voltage output from the amplifier 31 to the charged voltage of the capacitor Co is output from the output terminal OUT.
That is, the signal voltage supplied from the input terminal IN is applied to the base of the NPN transistor Q.sub.1 serving as the non-inverting input terminal of the gm amplifier 32 and to the base of the NPN transistor Q.sub.7 serving as the input terminal of the amplifier 31. Current flowing in the collector-emitter path of the transistor Q.sub.1 permits the transistor Q.sub.2 to be turned on via the resistor R.sub.1 and permits the transistor Q.sub.3 which is one of two transistors constituting the differential pair to be turned on. Further, since the transistor Q.sub.5 is always kept in the conductive state by means of the constant current source I.sub.3, the transistor Q.sub.6 is turned on by current flowing in the resistor R.sub.2 and the transistor Q.sub.4 which is the other of the two transistors constituting the differential pair is also turned on. The capacitor Co connected to the collector of the transistor Q.sub.4 is charged or discharged by a current difference between the collector currents of the transistors Q.sub.3 and Q.sub.4 and an output signal can be derived from the output terminal OUT. Further, the output signal is fed back to the inverting input terminal of the gm amplifier 32.
In the amplifier 31, the transistor Q.sub.8 is biased by the reference voltage Vo and is always kept in the on state and the transistor Q.sub.9 is biased by current flowing in the resistor R.sub.4 and is turned on. If a signal is input to the input terminal IN in this state, the transistor Q.sub.7 is turned on. Since the resistor R.sub.3 is connected between the emitters of the transistors Q.sub.7 and Q.sub.8, the current flowing in the transistor Q.sub.8 may be varied by means of the resistor R.sub.3 when the emitter current of the transistor Q.sub.7 is changed according to the input signal. The operation of the transistor Q.sub.9 biased by the resistor R.sub.4 is controlled according to variation in the emitter current of the transistor Q.sub.8. An amount of charge stored in the capacitor Co varies with variation in the emitter current of the transistor Q.sub.9.
In practice, a signal which is obtained by converting a voltage into current by means of the gm amplifier 32 may affect not only the capacitor Co but also the output terminal of the amplifier 31 via the emitter resistor r.sub.9 (not shown) of the transistor Q.sub.9. As a result, a signal output from the output terminal OUT is deviated from a theoretical value. Further, in a case where the capacitor Co is charged according to a signal voltage supplied to the input terminal IN and the charged voltage is added to the signal obtained by converting the voltage into the current, the signal may be made unstable by the emitter resistor r.sub.9 of the transistor Q.sub.9 and the collector impedance Ro of the transistor Q.sub.4.
In order to explain the above defects, the transfer function of the circuit having the construction shown in FIG. 4 is shown by the following equation. In this case, the emitter resistor of each transistor Qn is indicated by r.sub.n (n=7, 8, 9) and the collector impedance of the transistor Q.sub.4 is indicated by Ro. Further, if the conductance of the gm amplifier is denoted by gmo, the input voltage is denoted by Vin and the output voltage is denoted by Vout, then the relation between them can be expressed by the following equation. ##EQU1##
The above equation (1) can be rewritten as follows: ##EQU2##
If 1/j.omega.Cogmo=n/s, R.sub.4 /(r.sub.7 +r.sub.8 +R.sub.3)=m, R.sub.9 /gmo=a, and j.omega.CoRo/{1+(Ro+r.sub.9)j.omega.Co)=b, then the equation (2) can be rewritten as follows: ##EQU3##
In this case, the transfer function Vout/Vin can be expressed as follows: ##EQU4##
As shown in the above equation (4), the signal becomes equal to the theoretical value only when a=0 and b=1, and this condition is satisfied when the emitter resistor r.sub.9 of the transistor Q.sub.9 in FIG. 4 is neglected and the collector impedance of the transistor Q.sub.4 is regarded as being infinite.
As has been described, in the conventional active filter, the amplifier 31 is connected to the gm amplifier 31 by means of the capacitor Co. The amplifiers 31 and 32 inevitably interfere with each other. Consequently, the magnitude of the signal output by the active filter deviates from the theoretical value.